This article makes no sense whatsover. The Europeans pay for their oil with Euros now -- that is, they spend Euros to purchase dollars and then spend the dollars for oil.
Nice diversion from the part that does make sense.... they will not have to buy and hold dollars. If they do not buy and hold dollars, there is less demand for dollars. With the same or growing supply of dollars but less demand for them, the dollar in theory will drop in value.
They only hold the dollars for as long as it takes to buy the oil. The transaction probably takes 30 minutes max.